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Regulation Model: Geometrical Interpretation The (u mi ) i define separating hyperplanes Classification criterion is the inner product: Each datapoint is given the label of the hyperplane it is the furthest away from, on its positive side.

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Erroneous interpretation of the parameters Segal et al claim that: When u mi = 0, motif i is inactive in module m When u mi > 0 for all i,m, then only the presence of motifs is significant, not their absence

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Erroneous interpretation of the parameters Segal et al claim that: When u mi = 0, motif i is inactive in module m When u mi > 0 for all i,m, then only the presence of motifs is significant, not their absence Contradict normalisation conditions!

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Sparsity Sparsity can be understood as pruning Pruning can improve generalisation performance (deals with overfitting both by damping and by decreasing the degrees of freedom) Pruning ought not be seen as a combinatorial problem, but can be dealt with appropriate prior distributions Reconceptualise the problem:

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Sparsity: the Laplacian How to prune using a prior: choose a prior with a simple discontinuity at the origin, so that the penalty term does not vanish near the origin every time a parameter crosses the origin, establish whether it will escape the origin or is trapped in Brownian motion around it if trapped, force both its gradient and value to 0 and freeze it Can actively look for nearby zeros to accelerate pruning rate

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Probabilistic Relational Models GENES g.S 1, g.S 2,... g.R 1, g.R 2,... g.M g.E 1, g.E 1,... this variable cannot be considered an attribute of a gene, because it has attributes of its own that are gene-independent

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Future research 2. Model Selection Techniques improve interpretability learn the optimal number of modules in our model Are such methods consistent? Do they carry over just as well in PRMs?

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Future research 3. Fine tune the Laplacian regulariser to fit the skewing of the model

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Future research 4. The choice of encoding the question into a BN/PRM is only partly determined by the domain Are there any general ‘rules’ about how to restrict the choice so as to promoter interpretability?